1. Field of the Invention
The present invention is related to the apparatus for constructing cylindrical articles from a flat piece of sheet material, and provides means for constructing a pattern having parallel, opposite seam-defining edges connected by a curved end edge, wherein the seam-defining edges are adapted to be placed in abutting relationship with one another to define a cylindrical article having longitudinal elements of varying length, each of which are parallel to the axis of the cylinder, and wherein the curved end-edge of the pattern defines an oblique plane which passes through the cylinder and intersects the base plane thereof at an acute angle.
2. Description of the Prior Art
Generally, solids fall into three broadly defined classes: (1) those having parallel longitudinal elements, such as cylinders, rectangular prisms and the like; (2) those having radial longitudinal elelments, each of which intersect at a common point or vertex, such as cones, pyramids and the like; and (3) those having both parallel and radial elements, generally referred to as irregular solids.
Articles such as hollow, tubular ducts and the like, have outer surfaces or boundaries which define solids and therefore, may be categorized as falling into one of these classified cations. The articles may, in general, be fabricated from two-dimensional sheet patterns which are laid-out upon flat pieces of formable material such as sheet metal and the like.
Over the years three distinct methods have been developed for constructing the two-dimensional sheet patterns which, when assembled, define said articles. The first method is referred to as parallel line development and is useful in constructing sheet patterns of articles having parallel longitudinal elements. The second method is referred to as radial line development and is useful in constructing sheet patterns of articles having radial longitudinal elements. The third method, triangulation, is a general method of construction and may be utilized to construct sheet patterns for any article having at least one straight element extending the full length thereof. Generally, triangulation is limited to use in construction of patterns for articles which are classified as irregular solids. Each of these methods requires the projection of the "true length" of various elements of the article onto an "unrolled" or flat surface of sheet material which, when assembled, defines the outer surface of the article. Each of the required number of elements must be separately and precisely projected onto the pattern piece if an accurate article is to be constructed. A complete disclosure of each of these methods is found in: Elements of Sheet-Metal Work, chapters 4-6, by W. Cookson and A. Bold, published by Frederick J. Drake and Co., Chicago, Ill., 1939.
Further, it has been found that the sheet pattern for a two-piece, right-angle cylindrical elbow having pieces which intersect at a 45.degree. angle may be accurately developed utilizing the particular mathematical relationship derived from the specific geometric configuration thereof. Specifically, a circular cross-section of the elbow is subdivided into a plurality of equal sectors, each of which intersects the diameter at a specific angle "a.sub.n ". The stretch-out "S" is derived from: EQU S = .pi. D,
where "D" is the diameter of the circular cross-section. A line equal in length to the stretch-out S is constructed on a sheet of pattern material and is subdivided by lines normal thereto into a number of equal segments corresponding to the number of sectors of the circular cross-section. The curve which defines the plane of intersection of the elbow pieces is then constructed by determining those points on the curve which fall on the normal lines, wherein: EQU d.sub.n = D/2(1-SINa.sub.n),
wherein d equals the distance along a specific normal line n from the stretch-out line to the point on the curve. This method is fully disclosed in: Sheet Metal Pattern Layouts, pages 1021-1023, by Edwin P. Anderson, published by Theodore Audel and Co., New York, N.Y., 1965 (1969 printing).
While each of these methods produces a pattern which is generally of sufficient accuracy to fabricate a satisfactory article of the specific type described, it will be noted that the entire process must be repeated each time at least one dimension of the final article is altered.